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"Can you think of players who had excellent 'per-36-minute' stat lines on limited
minutes, and who either outperformed or seriously underperformed those 'per-36'
numbers once given an increase in minutes?

I'm a Celtics fan, so Glen Davis comes to mind as being a good example of
someone who produced close to their per-36 averages upon being given a larger
role.

I'm curious about some of the extremes; players whose averages were seriously
impacted by an increase in minutes. Basically examples that make you think, 'it
was a bad idea to give this guy more minutes' OR 'I can't believe he's been
coming off the bench all this time instead of starting!'"

One of the big early battlegrounds of APBRmetrics was the philosophical debate between per-minute and per-game statistics. Per-game was the traditional standard, but analysts like John Hollinger began to tear that way of thinking down after realizing per-minute performance held over for most players who received more playing time. From Hollinger's seminal 2004-05 Pro Basketball Forecast:

"It's a pretty simple concept, but one that has largely escaped most NBA front offices: The idea that what a player does on a per-minute basis is far more important than his per-game stats. The latter tend to be influenced more by playing time than by the quality of play, yet remain the most common metric of player performance.

[...]

Unfortunately, many NBA execs and fans still believe that somebody can be a '20 minute player' -- that he's only useful in short stretches but can't play a full game. With the exception of the rare few who are scandalously out of shape (Oliver Miller, for example), this is profoundly untrue. [Michael] Redd was the perfect example -- he was thought of as a bench player simple because that's what he'd always been, but there was no reason he couldn't play 40 minutes a night. There's a supposition that some players' production will decrease with increased minutes, but within reason that's completely untrue. The first Prospectus emphatically proved this with research showing that most player's [sic] performance improves with greater playing time."

Hollinger's examples of predictable "breakouts" from per-minute stats included Redd, Zach Randolph, Carlos Boozer, and Andrei Kirilenko, all of whom held onto their low-MPG production when thrust into bigger roles. In fact, Hollinger featured Redd on the cover of his 2nd book as an example of a player with great per-minute stats who was underrated because of a lack of playing time.

So, to answer Rob's original question, and in honor of Hollinger's early per-minute darlings, here are the "Redd-Randolph All-Stars". To qualify, a player had to:

play in the "Hollinger Era" (the 1990s, 2000s, or 2010s)

play at least 41 games in back-to-back seasons

play less than 24 MPG in the first of the back-to-back seasons, and more than 24 MPG in the second

see an increase of at least 7 MPG between the two seasons

Of that group (which included 320 players since 1990), I'll list 3 top-5 lists: players who improved their PERs the most when given increased playing time, players whose PERs were the closest to what they had been before when given increased playing time, and players whose PERs declined the most with an increase in PT. This will capture all of the possible extremes Rob mentioned, plus the Hollinger prototype of players whose PERs didn't change at all.

Note that all of the 5 players whose PERs most "stayed the same" played for the same team both seasons, while 6 of the 10 players at the extremes played season #2 in a different uniform than season #1. Further anecdotal evidence that a player's rate stats can go haywire when he changes teams.

And as for the eponymous Redd and Randolph? Each had one qualified season apiece:

My basic rationale was simple: this was originally a Hollinger concept, and I quoted him at length in the post, so it seemed fitting to use PER as the metric as well. Besides, PER is a decent way to summarize pts/36, reb/36, ast/36, etc. in one number, which is what I needed. Use SPM or WS/48 and you might accidentally take defense into account. :)

A tool for every task - I agree with Neil that PER makes for a decent summary of box score efficiency, one that represents a player's offense a lot more than defense despite the inclusion of blocks, steals and rebounds in the metric.

As for the post above, I only remember the tail end of the per-game versus per-minute debate. In retrospect it seems pretty amazing that there was a lot of resistance to that idea. Maybe in five years we'll look back on some present debate or point of contention and wonder at how we thought back then.

Kevin Love should send Hollinger a box of chocolates. He's the latest example of a massively under-used resource that did just fine when his minutes were pushed up. People wondered if this kid could still rebound 20% in starter's minutes when he was a rookie - and of course he did in late '09 and early '10, before winding up on the bench again and under 27 MPG to end the year.

Regarding per minute stats, I think it's a great idea in general, since player mpg can vary so dramatically. BUT, when it comes to evaluating elite players, like MVP candidates or the "Top 50" types, I think it's worthwhile to look at total production and per game production.

How about a grpahic, maybe a boxplot of the distribution here? Based on this post it seems Holligner was both right and wrong, namely, it's a coin toss. And one that may more be linked to changing jerseys as well as minutes? I'll also echo an above comment to see this based on some other metric, like boxplots of per minute values of REB, PTS, etc... One thing I've always wondered about is when the minutes boost occurs. If it's early on in a career there is a confounding age effect too, young players certainly can get better.

What David said about age certainly applies here. Guys at age 21/22/23 are supposed to get better. That Houston or Diaw or Martin got better was likely completely coincidental with the increase in minutes. So I am not buying this very much.

The Mikki Moore example is pretty interesting. It doesn't really show an increase in the player's ability so much as the value of being in the exact right situation. Pair Mikki Moore with Jason Kidd's ability to get him the ball in the perfect position and - voila - huge increase in production. But look at Mikki's next year, after he signed with GSW, and his production drops back down to what it was before he played with J-Kidd.

#6 - Completely agree. Per-minute and per-possession metrics are great because they give an indication of efficiency and potential. Per game shows actual production, which when trying to weigh elite starters is useful - always of course keeping in mind pace and play-style.

Whenever I thought of this question, two reasons I hesitated to assume that per-minute was superior to per-game were quality of competition and sample size.

For the former, a guy who is playing back-up minutes may be playing primarily against other back-ups. This will tend to inflate his stats. For the latter, if a guy is on the real low end of MPs (I'm thinking more under 10 then under 24), it is harder to trust the data because of the shallowness of the sample size. Obviously, this could impact his stats in either direction, with them being artificially low or high.

Other issues at play have to do with "rhythm" players, which I realize is a thorougly contested theory but I do not know if there is enough evidence to deny it out of hand and, more generally speaking, the need for players to get into the flow of the game. As a player, I would argue that coming in for 10 2-minute bursts is appreciably different from coming in for 2 10-minute bursts. So it is possible that how a player is used would impact his per-minute stats especially if he is on the low end of MPs.

What I think we really need to know is what percentage of total players fall into each group? Obviously, there were going to be some in each. But knowing the top 5 doesn't really help us figure out if per-minute or per-game is the preferred method. I think it'd be much more helpful to know how many guys remained consistent, got better, or got worse.

I actually wasn't really trying to prove something one way or another on the per-minute/per-game battle (I thought per-minute won that years ago anyway)... Rob asked for a list of players who fit each category, so my main goal was just to come up with some names. But if you guys want me to research this rigorously, I can try in a future post.

In the meantime, here is a graph of all 320 players who met the criteria I laid out (x-axis is increase in minutes per game, y-axis is change in PER):

Selection bias is a huge problem in any study like this, though, because the coach isn't playing a guy more for the purposes of our experiments (wouldn't that be great?), he's playing him more because he detects some improvement in skill.

Sorry if I misunderstood the purpose of this post. I didn't mean to make untold demands.

My hunch here is to draw the same conclusions here that I do with similar arguments in baseball, namely that rate stats are a better predictive tool (by a large margin) and bulk stats are a better reporting tool (by a slight margin). What I mean by "reporting tool" is one that tells me what happened. Knowing a guy had a PER of 15 doesn't really tell me anything about what he did that year, outside of the fact that he proved to be a reasonably effecient player. Knowing a guy scored 30 points a game or 2000 points for the season tells me what the guy actually did, even if it lacks the context to most effectively evaluate those numbers. On the other hand, knowing a guy scored 30 points a game doesn't really help me figure out what he'll do the next year, especially if his situation is changing. Knowing more about how he scored those points and how his new context compares to his old one is much more helpful in predicting future results.

Of course, this is a fairly amateur opinion and I'd be curious to hear other thoughts.

Rate stats -- especially SPM, where the weights are trying to predict the future more than assigning credit for the past -- are basically addressing Ability. They're predictive (we hope) of future productivity, in addition to explaining past per-minute/possession performance.

Counting stats sort of address Value... although as we've seen with the Derrick Rose debates, nobody can really agree on what 'value' means. I think the best approach for assessing past value is to use the VORP framework -- only rate stats above a certain threshold "count". It's a way to combine rate stats with playing time without favoring compilers, as pure counting stats are wont to do.

Neil - I'm with #8 here. Shouldn't there be an attempt to isolate age? All the younger players could have just improved their game, so it's hard to use that as a test of the per36 stats actually translating to full-minutes.

Thanks, Neil. That makes sense. There will also be subjective arguments around vague terms like "value". Even "ability" is debated at times.

The biggest issue I see is when people assume a stat is saying something it was not designed to do. If I say, "Player X led the league in scoring average with 35 points a game," there really isn't much to argue there. If we're trying to figure out who scored the most points per game, there is no better stat than PPG. If we're trying to figure out who is the best scorer or best offensive player... well, that's another conversation. Many will argue that PPG is still the ideal stat for that, but it is easy to point out the fallacies of such logic to those open to hearing it.

One thing that stand out between the list of players whose PERs improved and those whose stayed the same is age.

In the first batch, most of them experienced the jump in PER and minutes between season where they went from 21-22 or 22-23 in 3 of the 5 cases. One was a 24-25 season. Mikki Moore was the only real outlier. On the second list, the player are pretty consistently seeing the change between 23-24 and 24-25 seasons.

I know it's a small sample size, but this may show that the players vastly improving their PER improved due to a real increase in skill that one would expect from a young player putting in work on his game. However, the second list is comprised of more skilled players who simply were not getting the minutes they probably deserved in the first year.

Agrees with sportsjunkie, above. Age is a huge confounding factor here. Guys who get more minutes and improve from 21 to 22 are probably guys in their second year in the league, who we would expect to improve, anyway.

It would be interesting to add in a corrective factor for age/experience and where the player is on their career arc, and see if there is any correlation left over. My guess is that it would be pretty close to zero, but then, that sort of proves Hollinger's point.

How about a list of guys who got more minutes after being traded midseason, like Jordan Crawford, who has played about 23 MPG more for the Wizards than he did for the Hawks and has a PER change of +6.2 since the trade.

for probably your best data set for comparing per minute stats of players who see an increase in playing time en masse, just look at first year expansion teams - like 8081 dallas, 8889 charlotte and miami, 8990 minnesota and orlando, 9697 toronto and vancouver, 0405 charlotte...

As one user correctly pointed out, playing with Jason Kidd did wonders for Mikki Moore, just as it's doing wonders for Tyson Chandler (the millionaire's version).

Boris Diaw's huge improvement came because he stepped into Amare Stoudemire's shoes and played a huge offensive role. Diaw dropped back to normal once Stoudemire was healthy the following season.

The primary reason for backups (low minute players) to lose value when they enter the starting lineup (high minutes) is a change in USG%.

A high-volume guard like Nate Robinson becomes an entirely different player when going from minutes as a #1 option (as he was on the Knick bench) to the #4 option in Boston in an Eddie House type role.

Lou Williams is in a similar situation in Philly; he is the #1 option when he enters the game, and would not get as many scoring opportunities in the starting unit.

Or take Richard Jefferson, his production and PER is way down, but it's not because he's in declne, it's because he is the fourth option, as opposed to being the first or second.

Or perhaps the most obvious example: LeBron James, Dwyane Wade, and Chris Bosh. All three have PERs that declined, but it's not because they've individually declined (at least in LeBron and Wade's cases). Their PER may be down but the team is collectively better for it.

Unfortunately for the suggestions in #20 and #21, switching teams and situations is a pretty big confounding variable too. In lieu of the Dean Oliver Holy Grail of Basketball League where we are allowed to mix and match the best players for laboratory tests I think we have to try and find examples of a player getting a year-to-year increase in minutes whose not switching teams or roles and is older than 24. If there are any such examples.

I still haven't seen any attention paid to quality of opposition. If a backup plays largely against other backups and then is thrust into playing against starters, I can't help but assume this will have an impact.

Comparing single years to another single year is not necessarily how I would have done this. Players who play way above or way below their norms one year doesn't really inform the per-minute situation.

For almost all players yearly deviation is far more than career deviation. At least a three year sample is best for predictive capability I think.

Take the Moore example. He's at 9.5/8.0 in 2007, 13.4/7.0 in 2008. The next season when he plays the most minutes of his career and starts 79 games he's at 10.5/7.5. For just those three seasons he's at 11.1/7.3. And the year prior to these three, with the Clippers he was at 12.1/7.5.

Meanwhile, his career numbers are 11.5/7.7. 2007 was a down year, 2008 was an up year, 2009 was closer to norm.

Patently untrue that per minute stats wont translate to higher numbers?
I was thinking the conventional wisdom is right. Isn't that the whole point of guys like Iverson and Anthony, is that even though they take a lot of shots to get their points, other players won't produce at that level for that number of shots?

Note that all of the 5 players whose PERs most "stayed the same" played for the same team both seasons, while 6 of the 10 players at the extremes played season #2 in a different uniform than season #1. Further anecdotal evidence that a player's rate stats can go haywire when he changes teams.

Likewise, injuries -- Ford (spine, 2007-08), McDyess (shoulder, 2007), Bynum (hamstring,2010) -- or inflation (Mohammed, logged a 20.3 PER starting the last 28 games in a 25-win/2001 season for ATL after the trade from PHI where he was a more typical 15.3)...

Thanks so much for replying, Neil! I can't believe how thorough your search was.

Like Neil said, it was by my request that this post be generated. Clearly nothing was trying to be proven here. It was simply an exercise in uncovering the tremendous exceptions to the norm. I was interested in seeing the EXTREMES, the OUTLIERS.

Neil's "sub-group of 'PERs that stayed the same" seems to help illustrate that there are far more players whose PERs stay the same, and there are few players whose PERs are radically impacted by a change in minutes. ...So it's pretty appropriate for this to be termed "trivia," like Neil said.

I guess this is really just a stepping stone for a larger conversation, which seems to have broken out.

I, too, am interested in isolating age and team change as factors, but I wonder if that makes the window for this search too narrow for results to be of any particular interest. And at what point have you established too many arbitrary conditions for a search?

If you establish a minimum age, you do so because you assume players are still seriously developing their skills up to that point. However you'd also have to establish a maximum age because you assume that at a certain point a players skills begin to seriously decline, right? Is there another way to "isolate age" like #15 ElGee said?

Per-36 numbers ***MAY*** be accurate when you are talking about regular rotation players (6th/7th/8th men) moving into a larger role. BUT, I hear far too many people talk about their 11th-man "stud in the making" who's averaging 14/13/1/1/3 (per 36, of course!), when those minutes come almost exclusively against opposing teams' 2nd- and 3rd-string.

I find per 36 min stats especially useful for comparing a player's production over a number of seasons. Tim Duncan is a scary example. It's also useful when talking to someone who's obsessed with raw stats. Extrapolating from someone playing say 20 MPG to per 36 MPG is pretty reasonable.